Real-Time Identification of Wrist Kinematics via Sparsity-Promoting Extended Kalman Filter Based on Ellipsoidal Joint Formulation

Objective: This paper proposes a novel method for real-time wrist kinematics identification. Method: We design the wrist kinematics regression model following a novel ellipsoidal joint formulation, which features a quaternion-based rotation constraint and 2-dimensional Fourier linear combiners (FLC) to approximate the coupled rotations and translational displacements of the wrist. Extended Kalman Filter (EKF) is then implemented to update the model in real-time. However, unlike previous studies, here we introduce a sparsity-promoting feature in the model regression through the optimality of EKF by designing a smooth $\ell 1$-minimization observation function. This is done to ensure the best identification of key parameters, and to improve the robustness of regression under noisy conditions. Results: Simulations employ multiple reference models to evaluate the performance of the proposed approach. Experiments are later carried out on motion data collected by a lab-developed wrist kinematics measurement tool. Both simulation and experiment show that the proposed approach can robustly identify the wrist kinematics in real-time. Conclusion: The findings confirm that the proposed regression model combined with the sparsity-promoting EKF is reliable in the real-time modeling of wrist kinematics. Significance: The proposed method can be applied to generic wrist kinematics modeling problems, and utilized in the control system of wearable wrist exoskeletons. The framework of the proposed method may also be applied to real-time identification of other joints for exoskeleton control.